Location is known to affect the number, of a particular item, sold by heb pantry. Two different locations, a and b, are selected on an experimental basis. Location a was observed for 18 days and location b was observed for 18 days. The number of the particular items sold per day was recorded for each location. On average, location a sold 39 of these items with a sample standard deviation of 9 and location b sold 55 of these items with a sample standard deviation of 6. Does the data provide sufficient evidence to conclude that the true mean number of sales at location a exceeds the true mean number of sales at location b at the 0. 01 level of significance? select the [alternative hypothesis, value of the test statistic].

, μ1 − μ2 ≠ 0 and μ₁>μ₂ , that is true mean number of sales at location a is exceds than the true mean number of sales at location b at the 0. 1 level of significance.

We have given that

For Location A ,

sample size (n₁) = 18

standard deviations (s₁) = 9

sample mean (m₁) = 39

For Location B,

sample size (n₂) = 18

standard deviations (s₂) = 6

sample mean (m₂) = 55

0.01 level of significance implies confidence interval 1% .

1% Confidence interval for μ₁ - μ₂.

A t-test is used when looking at a numeric variable (such as height) and comparing the means of two different populations or groups.

Null Hypothesis

H0: μ₁ -μ₂= 0, where u1 is the first population mean and u2 is her second population mean.

As above, the null hypothesis tends to be no difference between the two population means. Or, more formally, that the difference is zero.

Equation , t =( m₁ - m₂ )/ (√(n₁ -1)s²₁ + (n₂- 1)s²₂)/(n₂ + n₁ - 2)( 1/n₁ + 1/n₂)

=> t = -16 /(√(17×81 + 17×36)/32 )(1/18 + 1/18)

=> t = - 16 /2.627

=> t = - 6.090

so, basis of t -value the null hypothesis is rejected.

hence , (μ₁ − μ₂ )not equal to 0 and t = - 6.090

t = (m₁ - μ₁ )/ s₁

=> -6.090 ×9 = 39 - μ₁

=>μ ₁ = 93.1

similarly, μ₂ = -6.090 ×6 + 55 = 91. 54

=> μ₁>μ₂

so, true mean number of sales at location a exceeds the true mean number of sales at location b.

To learn more about Null hypothesis on t - statistic, refer:

https://brainly.com/question/14016208

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